Stability of nonlinear systems with slow and fast time variation and switching: the common equilibrium case

Daniel Liberzon, Hyungbo Shim

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this paper we consider a class of nonlinear systems with two kinds of inputs: one is slowly-varying, the other is fast-varying and periodic, and both are only piecewise continuous. Under the assumption that the origin is a common equilibrium for all values of the input signals, we provide sufficient conditions under which this equilibrium is semi-globally exponentially stable. Our approach is based on considering the (partial) average system which averages out the fast variation but retains the slow variation, and which can be used to approximate the original system in a certain sense. The stability conditions involve the existence of a suitable Lyapunov function for this average system, along with a bound on the total variation of the slowly-varying input.

Original languageEnglish (US)
Title of host publication2024 IEEE 63rd Conference on Decision and Control, CDC 2024
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages5622-5627
Number of pages6
ISBN (Electronic)9798350316339
DOIs
StatePublished - 2024
Event63rd IEEE Conference on Decision and Control, CDC 2024 - Milan, Italy
Duration: Dec 16 2024Dec 19 2024

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0743-1546
ISSN (Electronic)2576-2370

Conference

Conference63rd IEEE Conference on Decision and Control, CDC 2024
Country/TerritoryItaly
CityMilan
Period12/16/2412/19/24

Keywords

  • Averaging
  • Lyapunov stability
  • Switched systems

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

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